PCA NMF Report for Chemicals

add two more columns: smoke_score and smoke_idicator

site map before cleaning with na

Clean the data

filter out all missing data if all chemicals are NA

filling zeros to all missing smoke value

Get the percentage of missing values for each chemicals

##            Hg EC_unadjusted        Na_ion            Co            Ag 
##     92.003298     81.088211     72.333059     72.305578     72.272602 
##            Ba            Cd            Ce            Cs            Sb 
##     72.272602     72.272602     72.272602     72.272602     72.272602 
##            Sn           NH4         K_ion        Cl_ion       nitrate 
##     72.272602     72.129706     72.129706     18.455620     15.147018 
##            OC            EC            Cl            Cu            Ni 
##     12.102226     11.673537      7.760374      7.716406      7.716406 
##            Cr            Fe            Br            As            Al 
##      7.710910      7.710910      7.694422      7.683430      7.683430 
##             P            Pb            Rb             S            Se 
##      7.683430      7.683430      7.683430      7.683430      7.683430 
##            Si            Sr            Zn            Zr            Ca 
##      7.683430      7.683430      7.683430      7.683430      7.677933 
##             K            Mn            Mg            Na            Ti 
##      7.677933      7.677933      7.677933      7.677933      7.677933 
##             V       sulfate 
##      7.677933      7.359165

The percentage of missing values in the dataset varies significantly across columns. Some columns, like ‘Hg’ and ‘EC_unadjusted’, have extremely high percentages of missing data (above 13%). For such columns, deletion might be the best approach since imputation could introduce substantial bias.

Delete columns with more than 13% missing data

now we will drop the row if the row contain any chemical that is missing.

data_update will not contain any missing chemical value.

get the map after cleanning data

updata data by using Guha we adjusted by all the data substrate minus data（background）

summary(chemical_column)

##        As                   Al                 Br                  Ca          
##  Min.   :-0.0010000   Min.   :-0.03900   Min.   :-0.003000   Min.   :-0.00300  
##  1st Qu.: 0.0000000   1st Qu.: 0.01700   1st Qu.: 0.001000   1st Qu.: 0.02700  
##  Median : 0.0000000   Median : 0.05000   Median : 0.002000   Median : 0.05610  
##  Mean   : 0.0002635   Mean   : 0.09667   Mean   : 0.002249   Mean   : 0.09916  
##  3rd Qu.: 0.0000000   3rd Qu.: 0.12000   3rd Qu.: 0.003000   3rd Qu.: 0.11700  
##  Max.   : 0.0270000   Max.   : 3.58620   Max.   : 0.071000   Max.   : 3.57200  
##        Cr                   Cu                  Cl                 Fe         
##  Min.   :-0.0050000   Min.   :-0.007000   Min.   :-0.00300   Min.   :-0.0040  
##  1st Qu.: 0.0000000   1st Qu.: 0.000000   1st Qu.: 0.00000   1st Qu.: 0.0346  
##  Median : 0.0000000   Median : 0.002000   Median : 0.00200   Median : 0.0710  
##  Mean   : 0.0006086   Mean   : 0.003809   Mean   : 0.02633   Mean   : 0.1079  
##  3rd Qu.: 0.0010000   3rd Qu.: 0.005000   3rd Qu.: 0.01300   3rd Qu.: 0.1410  
##  Max.   : 0.0560000   Max.   : 1.038400   Max.   : 3.31090   Max.   : 2.2560  
##        K                  Mn                  Mg                 Na          
##  Min.   :-0.00600   Min.   :-0.007000   Min.   :-0.02300   Min.   :-0.01800  
##  1st Qu.: 0.02700   1st Qu.: 0.001000   1st Qu.: 0.00000   1st Qu.: 0.00500  
##  Median : 0.04910   Median : 0.002000   Median : 0.01700   Median : 0.04900  
##  Mean   : 0.07958   Mean   : 0.002864   Mean   : 0.02775   Mean   : 0.09965  
##  3rd Qu.: 0.09200   3rd Qu.: 0.004000   3rd Qu.: 0.04000   3rd Qu.: 0.13000  
##  Max.   :30.12230   Max.   : 0.116000   Max.   : 2.43040   Max.   : 3.67300  
##        Ni                   P                  Pb           
##  Min.   :-0.0010000   Min.   :0.000000   Min.   :-0.011000  
##  1st Qu.: 0.0000000   1st Qu.:0.000000   1st Qu.: 0.000000  
##  Median : 0.0000000   Median :0.000000   Median : 0.001000  
##  Mean   : 0.0004088   Mean   :0.001115   Mean   : 0.002029  
##  3rd Qu.: 0.0004300   3rd Qu.:0.001000   3rd Qu.: 0.003000  
##  Max.   : 0.0326900   Max.   :0.207900   Max.   : 0.113000  
##        Rb                   S                Se                   Si         
##  Min.   :-0.0050000   Min.   :0.0000   Min.   :-0.0040000   Min.   :-0.0310  
##  1st Qu.: 0.0000000   1st Qu.:0.1290   1st Qu.: 0.0000000   1st Qu.: 0.0486  
##  Median : 0.0000000   Median :0.2223   Median : 0.0000000   Median : 0.1340  
##  Mean   : 0.0001558   Mean   :0.2782   Mean   : 0.0002728   Mean   : 0.2534  
##  3rd Qu.: 0.0003000   3rd Qu.:0.3604   3rd Qu.: 0.0003000   3rd Qu.: 0.3197  
##  Max.   : 0.0090000   Max.   :8.9036   Max.   : 0.0310000   Max.   : 6.5810  
##        Sr                  Ti                  V            
##  Min.   :-0.004000   Min.   :-0.003000   Min.   :0.0000000  
##  1st Qu.: 0.000000   1st Qu.: 0.002000   1st Qu.:0.0000000  
##  Median : 0.000900   Median : 0.005000   Median :0.0000000  
##  Mean   : 0.001256   Mean   : 0.007768   Mean   :0.0009102  
##  3rd Qu.: 0.001645   3rd Qu.: 0.010000   3rd Qu.:0.0010000  
##  Max.   : 0.494200   Max.   : 0.852000   Max.   :0.3000000  
##        Zn                  Zr                   OC               EC        
##  Min.   :-0.002000   Min.   :-0.0310000   Min.   :-0.060   Min.   :-0.010  
##  1st Qu.: 0.002000   1st Qu.: 0.0000000   1st Qu.: 0.648   1st Qu.: 0.130  
##  Median : 0.005000   Median : 0.0001000   Median : 1.160   Median : 0.310  
##  Mean   : 0.008445   Mean   : 0.0009404   Mean   : 1.798   Mean   : 0.549  
##  3rd Qu.: 0.010840   3rd Qu.: 0.0010000   3rd Qu.: 2.110   3rd Qu.: 0.710  
##  Max.   : 0.304000   Max.   : 0.0460000   Max.   :63.510   Max.   :16.510  
##     sulfate       
##  Min.   :-0.0100  
##  1st Qu.: 0.3510  
##  Median : 0.6050  
##  Mean   : 0.7717  
##  3rd Qu.: 0.9939  
##  Max.   :25.3841

background_levels

##      As      Al      Br      Ca      Cr      Cu      Cl      Fe       K      Mn 
##  -0.001  -0.039  -0.003  -0.003  -0.005  -0.007  -0.003  -0.004  -0.006  -0.007 
##      Mg      Na      Ni       P      Pb      Rb       S      Se      Si      Sr 
##  -0.023  -0.018  -0.001   0.000  -0.011  -0.005   0.000  -0.004  -0.031  -0.004 
##      Ti       V      Zn      Zr      OC      EC sulfate 
##  -0.003   0.000  -0.002  -0.031  -0.060  -0.010  -0.010

# To count negative values in each column
negative_counts <- apply(chemical_column, 2, function(x) sum(x < 0))
negative_counts

##      As      Al      Br      Ca      Cr      Cu      Cl      Fe       K      Mn 
##       4     683     122       4     636     676     349       6       6     655 
##      Mg      Na      Ni       P      Pb      Rb       S      Se      Si      Sr 
##    1038     600     335       0    1007    1285       0    1032      61     896 
##      Ti       V      Zn      Zr      OC      EC sulfate 
##     209       0      14    1982       6      22       4

# simply checking how many minimum values for each vocs
colSums(chemical_column == 0)

##      As      Al      Br      Ca      Cr      Cu      Cl      Fe       K      Mn 
##   11992     750    2250       6    8793    3437    4231       2       3    1749 
##      Mg      Na      Ni       P      Pb      Rb       S      Se      Si      Sr 
##    2891    2573   10278   10690    3223    7382       6    8797      30    2874 
##      Ti       V      Zn      Zr      OC      EC sulfate 
##     426    8528     466    5297       2      65       0

#adjusting by subtracting the minimum value
adjusted_data_update <- as.data.frame(sapply(names(chemical_column), function(tracer){ 
  chemical_column[[tracer]] - background_levels[[tracer]]
}))

Also, I think that works for our case, since if the machine detects negative values, it means there may be some issue with that machine and we need to adjust it. I think we can use ‘adjusted by all the data substrate minus data then’ for data exploring, which allows us to switch the minimum to zero and change adjust all the data.

# simply checking how many minimum values for each vocs
colSums(adjusted_data_update == 0)

##      As      Al      Br      Ca      Cr      Cu      Cl      Fe       K      Mn 
##       4       2       2       2       2      12      12       2       2       2 
##      Mg      Na      Ni       P      Pb      Rb       S      Se      Si      Sr 
##      13       2     335   10690       2      16       6       4       2       8 
##      Ti       V      Zn      Zr      OC      EC sulfate 
##      10    8528       2       2       2      22       4

Site.Code<- data_update$Site.Code
smoke_indicator <- data_update$smoke_indicator
smoke_score <- data_update$smoke_score
adjusted_data_update <- cbind(Site.Code, smoke_indicator,smoke_score, adjusted_data_update)

we will choose three site as our example, Inyo:06-027-0002, Fresno:06-019-0011, Rubidoux: 06-065-8001, Seattle: 53-033-0080

The histogram of the smoke score for Inyodata_smoke_day

The histogram of the smoke score for Fresno_smoke_day

There is no smoke day in Rubidoux

The histogram of the smoke score for Seattle_smoke_day

nrow(Inyodata)

## [1] 1518

nrow(Fresno)

## [1] 923

nrow(Rubidoux)

## [1] 95

nrow(Seattle)

## [1] 2002

nrow(Inyodata_smoke_day)

## [1] 195

nrow(Fresno_smoke_day)

## [1] 116

nrow(Rubidoux_smoke_day)

## [1] 0

nrow(Seattle_smoke_day)

## [1] 95

There is no smoke day in Rubidoux

names(adjusted_data_update)

##  [1] "Site.Code"       "smoke_indicator" "smoke_score"     "As"             
##  [5] "Al"              "Br"              "Ca"              "Cr"             
##  [9] "Cu"              "Cl"              "Fe"              "K"              
## [13] "Mn"              "Mg"              "Na"              "Ni"             
## [17] "P"               "Pb"              "Rb"              "S"              
## [21] "Se"              "Si"              "Sr"              "Ti"             
## [25] "V"               "Zn"              "Zr"              "OC"             
## [29] "EC"              "sulfate"

check correlation for Inyo:06-027-0002, Fresno:06-019-0011, Rubidoux: 06-065-8001, Seattle: 53-033-0080

Inyodata

Fresnodata

There is no smoke day in Rubidoux

Seattleata

PCA for each Inyo:06-027-0002, Fresno:06-019-0011, Rubidoux: 06-065-8001, Seattle: 53-033-0080

# function for plot cordinate of each chemical after PCA
plot_pca_component <- function(pca_result, pc_number, plot_title = "") {
  # Extract loadings for the specified PC
  loadings_pc <- pca_result$rotation[, pc_number]
  
  # Convert to dataframe for ggplot2
  loadings_df <- data.frame(Chemical = names(loadings_pc), Loading = loadings_pc)
  
  # Generate the plot
  pca_plot <- ggplot(loadings_df, aes(x = Loading, y = reorder(Chemical, Loading))) + 
    geom_bar(stat = "identity", fill = "skyblue") +
    coord_flip() +  # Flip coordinates to make it horizontal
    labs(title = sprintf("Loadings of Chemical Components on PC%d in %s", pc_number, plot_title),
         y = "Chemical Component",
         x = "Loading") +
    geom_text(aes(label = sprintf("%.3f", Loading)), vjust = -0.3, color = "red", size = 2) +
    theme_minimal()
  
  return(pca_plot)
}

Inyodata

Plotting the variance explained by each principal component

scale(chemical_data) it has a mean of 0 and a standard deviation of 1.

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     3.5370 1.8321 1.44149 1.18635 1.03333 1.00235 0.99012
## Proportion of Variance 0.4633 0.1243 0.07696 0.05213 0.03955 0.03721 0.03631
## Cumulative Proportion  0.4633 0.5877 0.66461 0.71673 0.75628 0.79349 0.82980
##                           PC8    PC9    PC10    PC11   PC12    PC13    PC14
## Standard deviation     0.9454 0.8879 0.84514 0.70229 0.5923 0.52923 0.52035
## Proportion of Variance 0.0331 0.0292 0.02645 0.01827 0.0130 0.01037 0.01003
## Cumulative Proportion  0.8629 0.8921 0.91855 0.93682 0.9498 0.96019 0.97022
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.49321 0.42686 0.35348 0.29270 0.23148 0.19365 0.17467
## Proportion of Variance 0.00901 0.00675 0.00463 0.00317 0.00198 0.00139 0.00113
## Cumulative Proportion  0.97923 0.98597 0.99060 0.99377 0.99576 0.99715 0.99828
##                           PC22    PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.15109 0.08073 0.07746 0.07566 0.06538 0.03401
## Proportion of Variance 0.00085 0.00024 0.00022 0.00021 0.00016 0.00004
## Cumulative Proportion  0.99912 0.99936 0.99959 0.99980 0.99996 1.00000

## Warning: `qplot()` was deprecated in ggplot2 3.4.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

plot PC from 1-10 for Inyo

Inyodata only smoke data

Plotting the variance explained by each principal component

## Importance of components:
##                           PC1    PC2     PC3     PC4    PC5    PC6     PC7
## Standard deviation     3.9078 2.0971 1.37050 1.05794 0.9735 0.8585 0.74446
## Proportion of Variance 0.5656 0.1629 0.06957 0.04145 0.0351 0.0273 0.02053
## Cumulative Proportion  0.5656 0.7285 0.79804 0.83949 0.8746 0.9019 0.92241
##                            PC8     PC9    PC10   PC11    PC12    PC13    PC14
## Standard deviation     0.70732 0.67230 0.51982 0.4958 0.42813 0.35814 0.34303
## Proportion of Variance 0.01853 0.01674 0.01001 0.0091 0.00679 0.00475 0.00436
## Cumulative Proportion  0.94094 0.95768 0.96769 0.9768 0.98358 0.98833 0.99269
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.25943 0.21596 0.18571 0.13693 0.10828 0.07860 0.07071
## Proportion of Variance 0.00249 0.00173 0.00128 0.00069 0.00043 0.00023 0.00019
## Cumulative Proportion  0.99518 0.99691 0.99819 0.99888 0.99932 0.99955 0.99973
##                           PC22    PC23    PC24    PC25    PC26      PC27
## Standard deviation     0.05952 0.04245 0.03457 0.02236 0.01404 3.148e-16
## Proportion of Variance 0.00013 0.00007 0.00004 0.00002 0.00001 0.000e+00
## Cumulative Proportion  0.99986 0.99993 0.99997 0.99999 1.00000 1.000e+00

plot PC from 1-10 for Inyo smoke day

Inyodata only nosmoke data

Plotting the variance explained by each principal component

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     3.4107 1.6956 1.35277 1.14595 1.07200 1.03226 1.01271
## Proportion of Variance 0.4309 0.1065 0.06778 0.04864 0.04256 0.03946 0.03798
## Cumulative Proportion  0.4309 0.5373 0.60511 0.65375 0.69631 0.73578 0.77376
##                           PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.9665 0.94638 0.88423 0.84622 0.76671 0.68464 0.67184
## Proportion of Variance 0.0346 0.03317 0.02896 0.02652 0.02177 0.01736 0.01672
## Cumulative Proportion  0.8084 0.84153 0.87049 0.89701 0.91879 0.93615 0.95286
##                           PC15    PC16    PC17   PC18    PC19    PC20    PC21
## Standard deviation     0.58853 0.56116 0.40519 0.3526 0.32153 0.26170 0.24220
## Proportion of Variance 0.01283 0.01166 0.00608 0.0046 0.00383 0.00254 0.00217
## Cumulative Proportion  0.96569 0.97735 0.98344 0.9880 0.99187 0.99441 0.99658
##                           PC22    PC23   PC24    PC25    PC26    PC27
## Standard deviation     0.21931 0.12935 0.1038 0.09567 0.07180 0.04992
## Proportion of Variance 0.00178 0.00062 0.0004 0.00034 0.00019 0.00009
## Cumulative Proportion  0.99836 0.99898 0.9994 0.99972 0.99991 1.00000

plot PC from 1-10 for Inyo nosmoke day

Fresnodata

## Importance of components:
##                           PC1    PC2     PC3    PC4     PC5     PC6     PC7
## Standard deviation     3.3799 1.8634 1.51541 1.3135 1.05494 0.96924 0.90797
## Proportion of Variance 0.4231 0.1286 0.08505 0.0639 0.04122 0.03479 0.03053
## Cumulative Proportion  0.4231 0.5517 0.63676 0.7007 0.74188 0.77667 0.80720
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.89924 0.80360 0.74175 0.69201 0.65916 0.63606 0.61355
## Proportion of Variance 0.02995 0.02392 0.02038 0.01774 0.01609 0.01498 0.01394
## Cumulative Proportion  0.83715 0.86107 0.88145 0.89918 0.91528 0.93026 0.94420
##                           PC15    PC16   PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.57879 0.56128 0.4876 0.39322 0.36843 0.33159 0.30691
## Proportion of Variance 0.01241 0.01167 0.0088 0.00573 0.00503 0.00407 0.00349
## Cumulative Proportion  0.95661 0.96828 0.9771 0.98281 0.98784 0.99191 0.99540
##                           PC22    PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.24596 0.15311 0.14280 0.11161 0.06982 0.05109
## Proportion of Variance 0.00224 0.00087 0.00076 0.00046 0.00018 0.00010
## Cumulative Proportion  0.99764 0.99851 0.99926 0.99972 0.99990 1.00000

plot PC from 1-10 for Fresno

Fresno only smoke data

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     3.9027 1.6896 1.41810 1.29468 0.97267 0.90009 0.76581
## Proportion of Variance 0.5641 0.1057 0.07448 0.06208 0.03504 0.03001 0.02172
## Cumulative Proportion  0.5641 0.6698 0.74433 0.80641 0.84145 0.87146 0.89318
##                            PC8     PC9    PC10    PC11   PC12    PC13    PC14
## Standard deviation     0.71175 0.59187 0.55449 0.54625 0.4902 0.46018 0.44899
## Proportion of Variance 0.01876 0.01297 0.01139 0.01105 0.0089 0.00784 0.00747
## Cumulative Proportion  0.91194 0.92492 0.93630 0.94736 0.9563 0.96410 0.97157
##                           PC15    PC16    PC17   PC18   PC19   PC20    PC21
## Standard deviation     0.41630 0.38362 0.33120 0.3076 0.2600 0.2543 0.19827
## Proportion of Variance 0.00642 0.00545 0.00406 0.0035 0.0025 0.0024 0.00146
## Cumulative Proportion  0.97799 0.98344 0.98750 0.9910 0.9935 0.9959 0.99736
##                           PC22    PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.18611 0.12347 0.11284 0.08076 0.03775 0.02789
## Proportion of Variance 0.00128 0.00056 0.00047 0.00024 0.00005 0.00003
## Cumulative Proportion  0.99864 0.99921 0.99968 0.99992 0.99997 1.00000

plot PC from 1-10 for Fresno_smoke

Fresno only nosmoke data

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6    PC7
## Standard deviation     3.0800 2.1040 1.53547 1.36223 1.10325 0.98823 0.9367
## Proportion of Variance 0.3513 0.1640 0.08732 0.06873 0.04508 0.03617 0.0325
## Cumulative Proportion  0.3513 0.5153 0.60262 0.67135 0.71643 0.75260 0.7851
##                            PC8    PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.90855 0.8817 0.82420 0.77168 0.71559 0.67124 0.65141
## Proportion of Variance 0.03057 0.0288 0.02516 0.02206 0.01897 0.01669 0.01572
## Cumulative Proportion  0.81567 0.8445 0.86962 0.89168 0.91064 0.92733 0.94305
##                          PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.6038 0.59346 0.52879 0.41336 0.32737 0.29177 0.24872
## Proportion of Variance 0.0135 0.01304 0.01036 0.00633 0.00397 0.00315 0.00229
## Cumulative Proportion  0.9566 0.96959 0.97995 0.98628 0.99025 0.99340 0.99569
##                           PC22   PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.19842 0.1721 0.14503 0.12829 0.08026 0.05848
## Proportion of Variance 0.00146 0.0011 0.00078 0.00061 0.00024 0.00013
## Cumulative Proportion  0.99715 0.9982 0.99903 0.99963 0.99987 1.00000

plot PC from 1-10 for Fresno_nosmoke

Rubidouxdata

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     3.2454 2.2432 1.46070 1.41877 1.05925 0.96873 0.96545
## Proportion of Variance 0.3901 0.1864 0.07902 0.07455 0.04156 0.03476 0.03452
## Cumulative Proportion  0.3901 0.5765 0.65548 0.73003 0.77159 0.80634 0.84087
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.87298 0.76670 0.72480 0.66708 0.61288 0.56619 0.52410
## Proportion of Variance 0.02823 0.02177 0.01946 0.01648 0.01391 0.01187 0.01017
## Cumulative Proportion  0.86909 0.89086 0.91032 0.92680 0.94071 0.95259 0.96276
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.46857 0.41809 0.38282 0.32974 0.28155 0.25235 0.23181
## Proportion of Variance 0.00813 0.00647 0.00543 0.00403 0.00294 0.00236 0.00199
## Cumulative Proportion  0.97089 0.97737 0.98279 0.98682 0.98976 0.99211 0.99411
##                           PC22    PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.22089 0.18288 0.17071 0.15953 0.11362 0.09707
## Proportion of Variance 0.00181 0.00124 0.00108 0.00094 0.00048 0.00035
## Cumulative Proportion  0.99591 0.99715 0.99823 0.99917 0.99965 1.00000

plot PC from 1-10 for Rubidoux （we don’t have non_smoke day for Rubidoux）

Seattledata

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     2.9193 1.9051 1.45708 1.34390 1.20689 1.06265 1.04374
## Proportion of Variance 0.3156 0.1344 0.07863 0.06689 0.05395 0.04182 0.04035
## Cumulative Proportion  0.3156 0.4501 0.52868 0.59558 0.64952 0.69135 0.73169
##                            PC8     PC9    PC10    PC11   PC12   PC13    PC14
## Standard deviation     0.97835 0.92746 0.89204 0.81608 0.7583 0.7237 0.69182
## Proportion of Variance 0.03545 0.03186 0.02947 0.02467 0.0213 0.0194 0.01773
## Cumulative Proportion  0.76715 0.79900 0.82848 0.85314 0.8744 0.8938 0.91156
##                           PC15    PC16    PC17    PC18   PC19    PC20    PC21
## Standard deviation     0.61336 0.58014 0.54202 0.52518 0.5065 0.46229 0.43721
## Proportion of Variance 0.01393 0.01247 0.01088 0.01022 0.0095 0.00792 0.00708
## Cumulative Proportion  0.92550 0.93796 0.94884 0.95906 0.9686 0.97648 0.98356
##                           PC22   PC23    PC24    PC25    PC26    PC27
## Standard deviation     0.37632 0.3244 0.28149 0.26033 0.19184 0.11545
## Proportion of Variance 0.00524 0.0039 0.00293 0.00251 0.00136 0.00049
## Cumulative Proportion  0.98880 0.9927 0.99563 0.99814 0.99951 1.00000

plot PC from 1-10 for Seattle

Seattle only smoke data

## Importance of components:
##                           PC1    PC2    PC3    PC4     PC5     PC6    PC7
## Standard deviation     3.1319 2.2502 1.7059 1.2696 1.16760 1.13338 0.9539
## Proportion of Variance 0.3633 0.1875 0.1078 0.0597 0.05049 0.04758 0.0337
## Cumulative Proportion  0.3633 0.5508 0.6586 0.7183 0.76880 0.81637 0.8501
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.92061 0.79237 0.73157 0.61282 0.56268 0.50986 0.44836
## Proportion of Variance 0.03139 0.02325 0.01982 0.01391 0.01173 0.00963 0.00745
## Cumulative Proportion  0.88147 0.90472 0.92454 0.93845 0.95018 0.95981 0.96725
##                           PC15    PC16    PC17    PC18    PC19    PC20    PC21
## Standard deviation     0.42766 0.38769 0.37397 0.34187 0.30490 0.24875 0.20414
## Proportion of Variance 0.00677 0.00557 0.00518 0.00433 0.00344 0.00229 0.00154
## Cumulative Proportion  0.97402 0.97959 0.98477 0.98910 0.99254 0.99483 0.99638
##                           PC22    PC23   PC24    PC25    PC26    PC27
## Standard deviation     0.19399 0.17039 0.1159 0.09786 0.06798 0.05899
## Proportion of Variance 0.00139 0.00108 0.0005 0.00035 0.00017 0.00013
## Cumulative Proportion  0.99777 0.99885 0.9993 0.99970 0.99987 1.00000

plot PC from 1-10 for Seattle （smoke day only）

Seattle only nosmoke data

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     2.9324 1.8756 1.46665 1.36525 1.21147 1.05549 1.05056
## Proportion of Variance 0.3185 0.1303 0.07967 0.06903 0.05436 0.04126 0.04088
## Cumulative Proportion  0.3185 0.4488 0.52843 0.59747 0.65183 0.69309 0.73396
##                            PC8     PC9    PC10    PC11    PC12    PC13    PC14
## Standard deviation     0.97448 0.92419 0.86963 0.81364 0.75095 0.71129 0.69146
## Proportion of Variance 0.03517 0.03163 0.02801 0.02452 0.02089 0.01874 0.01771
## Cumulative Proportion  0.76913 0.80077 0.82878 0.85330 0.87418 0.89292 0.91063
##                           PC15    PC16    PC17    PC18   PC19    PC20   PC21
## Standard deviation     0.62260 0.58065 0.54596 0.53523 0.4847 0.45830 0.4348
## Proportion of Variance 0.01436 0.01249 0.01104 0.01061 0.0087 0.00778 0.0070
## Cumulative Proportion  0.92499 0.93747 0.94851 0.95912 0.9678 0.97560 0.9826
##                           PC22   PC23    PC24    PC25    PC26   PC27
## Standard deviation     0.40273 0.3247 0.28190 0.26087 0.20292 0.1158
## Proportion of Variance 0.00601 0.0039 0.00294 0.00252 0.00153 0.0005
## Cumulative Proportion  0.98861 0.9925 0.99546 0.99798 0.99950 1.0000

plot PC from 1-10 for Seattle （nosmoke day only）

Normalize the chemical column

#normalizing function
normalize_column <- function(column){
  background <- quantile(column, 0)
  max <- quantile(column, 0.99)
  return ((column - background)/(max - background))
}

normalize_chemical <- data_update

#Getting the Transpose
normalize_chemical <- sapply(data_update[, 11:37], normalize_column) #normalize the chemicals
normalize_chemical <- data.frame(normalize_chemical)
Site.Code <- data_update$Site.Code
smoke_indicator <- data_update$smoke_indicator
normalize_chemical <- cbind(Site.Code, smoke_indicator, normalize_chemical)

NMF for each Inyo:06-027-0002, Fresno:06-019-0011, Rubidoux: 06-065-8001, Seattle: 53-033-0080

Inyodata

use plot the reconstruction error for NMF to find the best rank

This is the sample code to show how to get the error

Inyodata_nmf_matrix <- as.matrix(Inyodata_nmf)
# Prepare variables to store results
components <- 1:20
errors <- numeric(length(components))

# Loop over the number of components
for (n in components) {
  set.seed(123456)
  nmf_result <- nmf(Inyodata_nmf_matrix, rank = n, .options = 'NMF.options(seed=123456)')
  reconstruction <- nmf_result@fit@W %*% nmf_result@fit@H
  error <- norm(Inyodata_nmf_matrix - reconstruction, type = "F")
  errors[n] <- error
}

## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")

## NMF algorithm: 'brunet'

## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ...

## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]

## NMF seeding method: random

## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 1$target[1] 0

## DEBUG::nmfModel -> Instantiate NMF model:NMFstd

## DEBUG::nmfModel -> Set factors in model:NMFstd

## DEBUG::seed -> using NMF model 'NMFstd'

## DEBUG::seed -> use seeding method: 'random'

## DEBUG::nmfModel -> Instantiate NMF model:NMFstd

## DEBUG::nmfModel -> Set factors in model:NMFstd

## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x113a55b90>

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## DONE (converged at 420/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done

## # NMF computation exit status ... OK

## 
## ## Running normal exit clean up ...

## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 2$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17c56b518>

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## DONE (converged at 480/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 3$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

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## DONE (converged at 450/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 4$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 800/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 5$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 520/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 6$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1010/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 7$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1420/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 8$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 690/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 9$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1110/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 10$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1130/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 11$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1370/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 12$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1270/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 13$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 980/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 14$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1110/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 15$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1320/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 16$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (stopped at 2000/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 17$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1280/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 18$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1710/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 19$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (converged at 1130/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK
## # NMF call: .local(x = x, rank = rank, method = method, seed = ..1, model = ..2, 
##       .options = "NMF.options(seed=123456)")
## NMF algorithm: 'brunet'
## # ** Current RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # Setting up RNG ... 
## # ** Original RNG settings:

## # RNG kind:  Mersenne-Twister / Inversion / Rejection 
## # RNG state: 10403L, 624L, ..., 449848215L [825a7345133c6f7869527d185527e323]

## # RNG setup: standard [using current RNG]
## NMF seeding method: random
## DEBUG::seed -> using model parameters:
## $model[1] "NMFstd"$rank[1] 20$target[1] 0
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::seed -> using NMF model 'NMFstd'
## DEBUG::seed -> use seeding method: 'random'
## DEBUG::nmfModel -> Instantiate NMF model:NMFstd
## DEBUG::nmfModel -> Set factors in model:NMFstd
## DEBUG::nmf -> Seed is of class: 'NMFfit'

## ## OPTIONS:
## # parallel: TRUE | track: TRUE   | debug: 123456 | garbage.collect: 50
## # RNGstream: TRUE
## <object of class: NMFStrategyIterative>
##  name: brunet [NMF]
##  objective: 'KL' 
##  model: NMFstd 
##  <Iterative schema>
##   onInit: none
##   Update: function (i, v, x, copy = FALSE, eps = .Machine$double.eps, ...)
##   Stop: 'connectivity'
##   onReturn: none

## DEBUG::Strategy Workspace -> initialize static workspace: NULL=<environment: 0x17bd2fbb8>

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## DONE (stopped at 2000/2000 iterations)

## DEBUG::NMFStrategyIterativeX::run -> Done
## # NMF computation exit status ... OK
## 
## ## Running normal exit clean up ... 
## # Restoring NMF options ... OK

## [1] 8.557657

choose 6

Inyodata smoke only

use plot the reconstruction error for NMF to find the best rank

## [1] 4.396097

choose 6

Fresno

use plot the reconstruction error for NMF to find the best rank

## [1] 14.81323

choose 6

Fresno smoke only

use plot the reconstruction error for NMF to find the best rank

## [1] 4.749112

choose 6

Rubidoux

use plot the reconstruction error for NMF to find the best rank

## [1] 5.235342

choose 6

grid.arrange(Rubidoux_nfmplt_1, Rubidoux_nfmplt_2, Rubidoux_nfmplt_3, Rubidoux_nfmplt_4, Rubidoux_nfmplt_5,  Rubidoux_nfmplt_6, Rubidoux_nfmplt_7, Rubidoux_nfmplt_8, Rubidoux_nfmplt_9, Rubidoux_nfmplt_10, ncol=2)

we don’t have data for Rubidoux smoke only

Seattle

use plot the reconstruction error for NMF to find the best rank

## [1] 23.34048

choose 6

Seattle smoke only

use plot the reconstruction error for NMF to find the best rank

## [1] 3.548952

choose 6